• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.6
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• pp.71-78
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• 1989

The imput-output relations for nonlinear systems can be explicitly represented by the Volterra series and they can be characterized by the Volterra kernels. This study is concerned with modeling an elastomer force-displacement relation due to step inputs by utilizing the truncated Volterra series. Since it is practically impossible to apply step inputs that have infinite slope at zero time, the loads due to constant penetration(displacement) rate followed by constant penetration inputs are measured as an alternative approach and estimated for step inputs and then utilized for the truncated Volterra series models. One second order and one third order truncated Volterra series models have been employed to model the force-displacement relation which is one of the prominent properties to characterize the viscoelastic material. The third order truncated Volterra series model has better results, compared with those of the second order truncated Volterra series model.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.11B
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• pp.1895-1902
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• 2000

이 논문에서는 AD 변화기의 앞에 설치되는 샘플-앤드-홀드 회로의 비선형성을 보상하기 위해 신경 회로망 기법과 볼테라 급수 모델을 직접적으로 적용하는 기법을 제안한다. 제안하는 기법들의 성능을 비교하기 위해, 볼테라 급수 모델에 기반을 둔 전통적인 p차 역산 방식의 결과와 비교 검토한다. 비교 검토를 위해서는 모노-톤과 투-톤 신호를 사용하여 출력의 고조파 및 혼변조 레벨을 살펴보았다. p차 역산 방식이 역 시스템을 구하는 것이라면 제안하는 기법들은 최적화 기법에 바탕을 두고 있다고 할 수 있다. 결과를 보면 어떤 한 방식이 다른 방식보다 성능이 월등하다고 할 수 없는데, 그 이유는 각 방식마다 나름대로의 장단점을 갖고 있기 때문이다. 보상 방식의 선택은 신호의 통계적 성질, 신호 레벨, 비선형성의 정도 등을 고려해야 한다.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.3 s.43
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• pp.33-42
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• 2005

Frequency domain Volterra model is applied to nonlinear parameter identification procedure for dynamic systems modeled by nonlinear function. The frequency domain Volterra kernels, which correspond io linear, quadratic, and cubic transfer functions in lime domain, are incorporated in nonlinear parametric identification procedure. The nonlinear transfer functions, which can be derived from the Volterra series representation of the nonlinear differential equation of the system by Schetzen's method(1980), are directly used for modeling input output relation. The error is defined by the difference between the observed output and the estimated output which is calculated by substituting the observed input to nonlinear frequency domain model. The system parameters are searched by minimizing the error. Volterra model guarantees enough accuracy and convergence and the estimated coefficients have a good agreement with their actual values not only in the linear frequency region but also in the legion where the $2^{nd}\;or\;3^{rd}$ order nonlinearity is dominant.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 1998.11a
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• pp.398-402
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• 1998

본 논문에서는 유ㆍ무선 통신 채널을 통한 데이터 전송시 발생하는 비선형 왜곡을 적응 필터를 이용하여 보상하였다. 특히 통신채널에서는 심볼간 간섭(ISI)이 발생하는데 이러한 간섭을 비선형 필터를 이용하여 제거하였다. 비선형 채널을 모델링하는 방법에는 볼테라급수를 이용하는 방법과 쌍선형 방법이 있다. 쌍선형 방법은 볼테라 방법에 비하여 계산량이 적은 장점을 지니고 있다. 따라서 쌍선형 필터에 적응 알고리듬을 적용하여 신호의 왜곡을 보상하였다. 적응 알고리듬에는 LMS 계열과 LS 계열 알고리듬이 있으나 통신 채널에서는 알고리듬의 안정도가 중요하므로 LMS 계열 알고리듬을 적용하였다. 또한 적응 알고리듬은 입력 데이터의 상관성과 데이터 수에 의존하여 수렴속도와 안정도가 결정된다. 알고리듬의 수렴속도를 증가시키기 위하여 입력신호를 신호파형으로부터 다량의 데이터를 검출하는 방법을 적용하였다. 이러한 방법을 입증하기 위하여 입력신호는 2진 랜덤 가우시안 데이터를 이용하였고, 통신채널에서 채널간 간섭을 발생시켰으며 화이트 가우시안 잡음을 부가 시켰다. 이러한 신호를 수신한 수신기에 적응 등화기를 설계하여 대량의 데이터를 생성시키고, 적응 알고리듬을 적용하여 채널의 왜곡을 빠른 속도로 보상하였다.

• Journal of the Society of Naval Architects of Korea
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• v.57 no.5
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• pp.305-311
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• 2020

This study presents a probabilistic time series forecast of ship structural response using Bayesian inference combined with Volterra linear model. The structural response of a ship exposed to irregular wave excitation was represented by a linear Volterra model and unknown uncertainties were taken care by probability distribution of time series. To achieve the goal, Volterra series of first order was expanded to a linear combination of Laguerre functions and the probability distribution of Laguerre coefficients is estimated using the prepared data by treating Laguerre coefficients as random variables. In order to check the validity of the proposed methodology, it was applied to a linear oscillator model containing damping uncertainties, and also applied to model test data obtained by segmented hull model of 400,000 DWT VLOC as a practical problem.

• Journal of the Society of Naval Architects of Korea
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• v.51 no.4
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• pp.274-282
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• 2014

Time series of the dynamic response of a slender marine structure was predicted using quadratic Volterra series. The wave-structure interaction system was identified using the NARX(Nonlinear Autoregressive with Exogenous Input) technique, and the network parameters were determined through the supervised training with the prepared datasets. The dataset used for the network training was obtained by carrying out the nonlinear finite element analysis on the freely standing riser under random ocean waves of white noise. The nonlinearities involved in the analysis were both large deformation of the structure under consideration and the quadratic term of relative velocity between the water particle and structure in Morison formula. The linear and quadratic frequency response functions of the given system were extracted using the multi-tone harmonic probing method and the time series of response of the structure was predicted using the quadratic Volterra series. In order to check the applicability of the method, the response of structure under the realistic ocean wave environment with given significant wave height and modal period was predicted and compared with the nonlinear time domain simulation results. It turned out that the predicted time series of the response of structure with quadratic Volterra series successfully captures the slowly varying response with reasonably good accuracy. It is expected that the method can be used in predicting the response of the slender offshore structure exposed to the Morison type load without relying on the computationally expensive time domain analysis, especially for the screening purpose.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.49 no.4
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• pp.9-17
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• 2012

In this paper, we show the memory effect of the high-power amplifiers for wied-band signals, present a compensation method for the nonlinearity combined with memory effect, and analyze its performance. For the modeling and the compensation of the nonlinear high-power amplifier with memory effect, we investigate the Volterra series model, the Wiener model, and the Hammerstein model. As a compensator scheme, we propose a digital feedforward technique. Compared to analog feed-forward scheme, the proposed scheme has better stability and adaptability to the environmental changes. It has a simpler structure than the conventional digital nonlinear compensation schemes. The result of computer simulations using ADS of the Agilent shows that spectral re-growth is suppressed by more than 20 dB, which amounts to at least 10 dB back-off. Considering the compensation performance, implementation complexity, and convergence rate, we could conclude the Wiener model is most suitable for the proposed scheme.